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Reaction mechanisms: Rate law
Related Topics
Wize University Chemistry Textbook > Kinetics
Reaction Mechanisms
7 Activities
Wize University Chemistry Textbook > Kinetics
The Rate Law
8 Activities
The rate law for the overall reaction A + 2B → E was experimentally determined to be:
Rate = k[A]
2
[B]
Which of these proposed mechanisms could explain this observed rate law?
Step 1 (slow): A
2
+ B → C
Step 2 (fast): C + B → E
Step 1 (slow): 2A + B → C
Step 2 (fast): C + B → E
Step 1 (slow): A + B → C
Step 2 (fast): C + B → E
Step 1 (slow): 2A + B → C
Step 2 (fast): C + B → E + A
Step 1 (slow): A
2
+ B → AB + A
Step 2 (fast): AB + B → E
I don't know
Check Submission
More Reaction Mechanisms Questions:
The decomposition of ozone to oxygen gas can also occur in the presence of chlorine atoms. A proposed mechanism for this exothermic reaction is as follows:
C
ℓ
(
g
)
+
O
3
(
g
)
→
C
ℓ
O
(
g
)
+
O
2
(
g
)
s
l
o
w
O
3
(
g
)
→
O
(
g
)
+
O
2
(
g
)
f
a
s
t
C
ℓ
O
(
g
)
+
O
(
g
)
→
C
ℓ
(
g
)
+
O
2
(
g
)
f
a
s
t
\begin{aligned}&C\ell(g)+O_3(g)\rightarrow C\ell O(g)+O_2(g)&slow\\ &O_3(g)\rightarrow O(g)+O_2(g)&fast \\&C\ell O(g)+O(g)\rightarrow C\ell(g)+O_2(g)&fast\end{aligned}
C
ℓ
(
g
)
+
O
3
(
g
)
→
C
ℓ
O
(
g
)
+
O
2
(
g
)
O
3
(
g
)
→
O
(
g
)
+
O
2
(
g
)
C
ℓ
O
(
g
)
+
O
(
g
)
→
C
ℓ
(
g
)
+
O
2
(
g
)
s
l
o
w
f
a
s
t
f
a
s
t
Which of these statements about this reaction is true?
The decomposition of ozone to oxygen gas can also occur in the presence of chlorine atoms. A proposed mechanism for this exothermic reaction is as follows:
C
ℓ
(
g
)
+
O
3
(
g
)
→
C
ℓ
O
(
g
)
+
O
2
(
g
)
s
l
o
w
O
3
(
g
)
→
O
(
g
)
+
O
2
(
g
)
f
a
s
t
C
ℓ
O
(
g
)
+
O
(
g
)
→
C
ℓ
(
g
)
+
O
2
(
g
)
f
a
s
t
\begin{aligned}&C\ell(g)+O_3(g)\rightarrow C\ell O(g)+O_2(g)&slow\\ &O_3(g)\rightarrow O(g)+O_2(g)&fast \\&C\ell O(g)+O(g)\rightarrow C\ell(g)+O_2(g)&fast\end{aligned}
C
ℓ
(
g
)
+
O
3
(
g
)
→
C
ℓ
O
(
g
)
+
O
2
(
g
)
O
3
(
g
)
→
O
(
g
)
+
O
2
(
g
)
C
ℓ
O
(
g
)
+
O
(
g
)
→
C
ℓ
(
g
)
+
O
2
(
g
)
s
l
o
w
f
a
s
t
f
a
s
t
Which of these statements about this reaction is true?
A proposed mechanism for the reaction of NO
2
with CO is shown below. Which of the given rate laws would accurately describe a reaction with this mechanism?
N
O
2
(
g
)
+
N
O
2
(
g
)
→
N
O
3
(
g
)
+
N
O
(
g
)
s
l
o
w
N
O
3
(
g
)
+
C
O
(
g
)
→
N
O
2
(
g
)
+
C
O
2
(
g
)
f
a
s
t
N
O
2
(
g
)
+
C
O
(
g
)
→
N
O
(
g
)
+
C
O
2
(
g
)
o
v
e
r
a
l
l
\def\arraystretch{1.5} \begin{array}{cc} NO_2(g)+NO_2(g)\to NO_3(g)+NO(g) & slow \\ NO_3(g)+CO(g)\to NO_2 (g) +CO_2 (g) & fast \\ \hline NO_2(g)+CO(g)\to NO(g)+CO_2(g) & overall \end{array}
N
O
2
(
g
)
+
N
O
2
(
g
)
→
N
O
3
(
g
)
+
N
O
(
g
)
N
O
3
(
g
)
+
C
O
(
g
)
→
N
O
2
(
g
)
+
C
O
2
(
g
)
N
O
2
(
g
)
+
C
O
(
g
)
→
N
O
(
g
)
+
C
O
2
(
g
)
s
l
o
w
f
a
s
t
o
v
er
a
l
l
Practice: Reaction Mechanisms
For the reaction:
2
N
O
C
l
(
g
)
⟶
2
N
O
(
g
)
+
C
l
2
(
g
)
R
a
t
e
e
x
p
=
k
[
N
O
C
l
]
2
2NOCl(g)⟶2NO(g)+Cl_2 (g)\qquad Rate_{exp}=k[NOCl]^2
2
N
O
C
l
(
g
)
⟶
2
N
O
(
g
)
+
C
l
2
(
g
)
R
a
t
e
e
x
p
=
k
[
N
O
C
l
]
2
The following three mechanisms have been proposed :
Rate Laws: Reaction Mechanisms
For the reaction:
2
N
O
C
l
(
g
)
⟶
2
N
O
(
g
)
+
C
l
2
(
g
)
R
a
t
e
e
x
p
=
k
[
N
O
C
l
]
2
2NOCl(g)⟶2NO(g)+Cl_2 (g)\qquad Rate_{exp}=k[NOCl]^2
2
N
O
C
l
(
g
)
⟶
2
N
O
(
g
)
+
C
l
2
(
g
)
R
a
t
e
e
x
p
=
k
[
N
O
C
l
]
2
The following three mechanisms have been proposed :
Collision Theory: Ozone
The decomposition of ozone to oxygen gas can also occur in the presence of chlorine atoms. A proposed mechanism for this exothermic reaction is as follows:
C
ℓ
(
g
)
+
O
3
(
g
)
→
C
ℓ
O
(
g
)
+
O
2
(
g
)
s
l
o
w
O
3
(
g
)
→
O
(
g
)
+
O
2
(
g
)
f
a
s
t
C
ℓ
O
(
g
)
+
O
(
g
)
→
C
ℓ
(
g
)
+
O
2
(
g
)
f
a
s
t
\begin{aligned}&C\ell(g)+O_3(g)\rightarrow C\ell O(g)+O_2(g)&slow\\ &O_3(g)\rightarrow O(g)+O_2(g)&fast \\&C\ell O(g)+O(g)\rightarrow C\ell(g)+O_2(g)&fast\end{aligned}
C
ℓ
(
g
)
+
O
3
(
g
)
→
C
ℓ
O
(
g
)
+
O
2
(
g
)
O
3
(
g
)
→
O
(
g
)
+
O
2
(
g
)
C
ℓ
O
(
g
)
+
O
(
g
)
→
C
ℓ
(
g
)
+
O
2
(
g
)
s
l
o
w
f
a
s
t
f
a
s
t
Which of these statements about this reaction is true?
A proposed mechanism for the reaction of NO
2
with CO is shown below. Which of the given rate laws would accurately describe a reaction with this mechanism?
N
O
2
(
g
)
+
N
O
2
(
g
)
→
N
O
3
(
g
)
+
N
O
(
g
)
s
l
o
w
N
O
3
(
g
)
+
C
O
(
g
)
→
N
O
2
(
g
)
+
C
O
2
(
g
)
f
a
s
t
N
O
2
(
g
)
+
C
O
(
g
)
→
N
O
(
g
)
+
C
O
2
(
g
)
o
v
e
r
a
l
l
\def\arraystretch{1.5} \begin{array}{cc} NO_2(g)+NO_2(g)\to NO_3(g)+NO(g) & slow \\ NO_3(g)+CO(g)\to NO_2 (g) +CO_2 (g) & fast \\ \hline NO_2(g)+CO(g)\to NO(g)+CO_2(g) & overall \end{array}
N
O
2
(
g
)
+
N
O
2
(
g
)
→
N
O
3
(
g
)
+
N
O
(
g
)
N
O
3
(
g
)
+
C
O
(
g
)
→
N
O
2
(
g
)
+
C
O
2
(
g
)
N
O
2
(
g
)
+
C
O
(
g
)
→
N
O
(
g
)
+
C
O
2
(
g
)
s
l
o
w
f
a
s
t
o
v
er
a
l
l
The proposed mechanism for a reaction is:
A
(
g
)
+
B
(
g
)
↔
X
(
g
)
(
F
a
s
t
)
A_{(g)}+B_{(g)} \leftrightarrow X_{(g)}(Fast)
A
(
g
)
+
B
(
g
)
↔
X
(
g
)
(
F
a
s
t
)
X
(
g
)
+
C
(
g
)
↔
Y
(
g
)
(
S
l
o
w
)
X_{(g)} +C_{(g)}\leftrightarrow Y_{(g)}(Slow)
X
(
g
)
+
C
(
g
)
↔
Y
(
g
)
(
S
l
o
w
)
Hydrogen spontaneously decomposes into two hydrogen atom radicals. One of these radicals reacts with an equivalent of fluorine gas to form one equivalent of HF and one fluorine atom. This fluorine atom reacts with a hydrogen atom to form another equivalent of HF. Write the mechanism of this reaction as series of elementary steps. Assign the molecularity of each step and write the overall reaction.
Collision Theory: Molecularity
Hydrogen spontaneously decomposes into two hydrogen atom radicals. One of these radicals reacts with an equivalent of fluorine gas to form one equivalent of HF and one fluorine atom. This fluorine atom reacts with a hydrogen atom to form another equivalent of HF. Write the mechanism of this reaction as series of elementary steps. Assign the molecularity of each step and write the overall reaction.
More The Rate Law Questions:
Rate Laws: Concentration
The reaction A + 2B → products was found to follow the rate law: rate = k[A]
2
[B]. Predict by what factor the rate of reaction will increase when the concentration of A is doubled, the concentration of B is tripled, and the temperature remains constant.
Rate Laws: Relative Rates of Reactions
Consider the balanced chemical equation for the reaction
2
C
O
(
g
)
+
O
2
(
g
)
⟶
2
C
O
2
(
g
)
R
a
t
e
=
k
[
C
O
]
2
2CO(g)+O_2(g)⟶2CO_2(g)\qquad Rate=k[CO]^2
2
C
O
(
g
)
+
O
2
(
g
)
⟶
2
C
O
2
(
g
)
R
a
t
e
=
k
[
C
O
]
2
If the rate of the reaction is 3.2 M/s which of the following is TRUE.
A proposed mechanism for the reaction of NO
2
with CO is shown below. Which of the given rate laws would accurately describe a reaction with this mechanism?
N
O
2
(
g
)
+
N
O
2
(
g
)
→
N
O
3
(
g
)
+
N
O
(
g
)
s
l
o
w
N
O
3
(
g
)
+
C
O
(
g
)
→
N
O
2
(
g
)
+
C
O
2
(
g
)
f
a
s
t
N
O
2
(
g
)
+
C
O
(
g
)
→
N
O
(
g
)
+
C
O
2
(
g
)
o
v
e
r
a
l
l
\def\arraystretch{1.5} \begin{array}{cc} NO_2(g)+NO_2(g)\to NO_3(g)+NO(g) & slow \\ NO_3(g)+CO(g)\to NO_2 (g) +CO_2 (g) & fast \\ \hline NO_2(g)+CO(g)\to NO(g)+CO_2(g) & overall \end{array}
N
O
2
(
g
)
+
N
O
2
(
g
)
→
N
O
3
(
g
)
+
N
O
(
g
)
N
O
3
(
g
)
+
C
O
(
g
)
→
N
O
2
(
g
)
+
C
O
2
(
g
)
N
O
2
(
g
)
+
C
O
(
g
)
→
N
O
(
g
)
+
C
O
2
(
g
)
s
l
o
w
f
a
s
t
o
v
er
a
l
l
Given the following data for the
N
H
4
+
+
N
O
2
−
→
N
2
+
2
H
2
O
NH_4^++NO_2^-→N_2+2H_2O
N
H
4
+
+
N
O
2
−
→
N
2
+
2
H
2
O
reaction, the rate law for the reaction is
T
r
i
a
l
[
N
H
4
+
]
[
N
O
2
–
]
R
a
t
e
1
0.010
M
0.030
M
0.020
M
/
s
2
0.015
0.030
0.030
3
0.010
0.015
0.005
\def\arraystretch{1.5} \begin{array}{c} Trial &[NH_4^+] &[NO_2^–]& Rate \\ \hline 1 & 0.010 M & 0.030 M &0.020 M/s \\ 2& 0.015& 0.030 &0.030 \\ 3&0.010 & 0.015 &0.005 \\ \end{array}
T
r
ia
l
1
2
3
[
N
H
4
+
]
0.010
M
0.015
0.010
[
N
O
2
–
]
0.030
M
0.030
0.015
R
a
t
e
0.020
M
/
s
0.030
0.005
Assume the following reaction occurs by the given reaction mechanism.
3
H
2
+
C
O
→
C
H
4
+
H
2
O
3H_2 +CO \to CH_4+H_2O
3
H
2
+
C
O
→
C
H
4
+
H
2
O
Step 1
H
2
+
C
O
→
H
2
C
O
H_2 +CO \to H_2CO
H
2
+
C
O
→
H
2
C
O
Slow
Rate Laws: Concentration
The reaction A + 2B → products was found to follow the rate law: rate = k[A]
2
[B]. Predict by what factor the rate of reaction will increase when the concentration of A is doubled, the concentration of B is tripled, and the temperature remains constant.
Rate Laws
The reaction A + 2B → products has been found to have the rate law, rate = k[A][B]
2
. While holding the concentration of A constant, the concentration of B is increased from
x
to
3x
. Predict by what factor the rate of reaction increases.
Rate Laws: Relative Rates of Reactions
Consider the balanced chemical equation for the reaction
2
C
O
(
g
)
+
O
2
(
g
)
⟶
2
C
O
2
(
g
)
R
a
t
e
=
k
[
C
O
]
2
2CO(g)+O_2(g)⟶2CO_2(g)\qquad Rate=k[CO]^2
2
C
O
(
g
)
+
O
2
(
g
)
⟶
2
C
O
2
(
g
)
R
a
t
e
=
k
[
C
O
]
2
If the rate of the reaction is 3.2 M/s which of the following is TRUE.
For the following elementary reactions apply the Law of mass balance to write a rate law, What is the overall order of the reaction? (Enter answer as 1st, 2nd, 3rd etc)
a)
B
2
H
6
→
2
B
H
3
\rm B_2H_6\quad\overrightarrow{\hspace{1.5cm}}\quad 2\ BH_3
B
2
H
6
2
B
H
3
b)
X
e
+
F
2
→
X
e
F
2
\rm Xe\quad+\quad F_2\quad\overrightarrow{\hspace{1.5cm}}\quad XeF_2
Xe
+
F
2
Xe
F
2
Hydrofluoric acid, HF, is a weak acid which exists as a gas. However HF is incredibly corrosive and can dissolve porcelain, metal, wood etc. Aqueous solutions of HF are featured on Breaking Bad as a method for disposing of bodies. If light is shone on HF in the gas phase it rapidly decomposes to H
2
and F
2
by the following mechanism.
a
a
a
2
H
F
→
H
2
+
F
2
a
a
a
‾
\underline{\textcolor{white}{aaa}2HF \to H_2+F_2\textcolor{white}{aaa}}
aaa
2
H
F
→
H
2
+
F
2
aaa
H
F
→
k
1
⋅
H
+
⋅
F
HF \xrightarrow{k_1} \cdot H + \cdot F
H
F
k
1
⋅
H
+
⋅
F
Which of the following has NO EFFECT on the rate of a zero-order reaction
Write a general rate law for the following elementary reactions
C
H
4
→
⋅
C
H
3
+
⋅
H
\rm CH_{4}\quad\overrightarrow{\hspace{1.5cm}}\quad \cdot CH_{3}\quad+\quad \cdot H
C
H
4
⋅
C
H
3
+
⋅
H
⋅
B
r
+
⋅
B
r
→
B
r
2
\rm \cdot Br\quad+\quad \cdot Br\quad\overrightarrow{\hspace{1.5cm}}\quad Br_{2}
⋅
Br
+
⋅
Br
B
r
2
The Rate Law
The graph below describes the reaction
A
→
B
A \rightarrow B
A
→
B
What is the slope of this line?
Determine an empirical rate law for the following reaction using the kinetic data collected at
298
K
298\ K
298
K
and evaluate the rate constant
k
k
k
. Report your k value with 2 sig figs and no units.
2
F
e
+
A
l
2
O
3
+
6
H
C
l
→
F
e
2
O
3
+
2
A
l
C
l
3
+
3
H
2
O
\rm 2\ Fe\quad+\quad Al_2O_3\quad+\quad6\ HCl\quad\overrightarrow{\hspace{1.5cm}}\quad Fe_2O_3\quad+\quad2\ AlCl_3\quad+\quad3\ H_2O
2
Fe
+
A
l
2
O
3
+
6
HCl
F
e
2
O
3
+
2
AlC
l
3
+
3
H
2
O
R
u
n
[
F
e
]
0
[
A
l
2
O
3
]
0
[
H
C
l
]
0
i
n
i
t
i
a
l
r
a
t
e
1
1.0
M
1.0
M
1.0
M
0.020
2
1.0
M
2.0
M
1.0
M
0.080
3
2.0
M
1.0
M
1.0
M
0.020
4
3.0
M
2.0
M
2.0
M
0.160
\begin{array}{|c|c|c|c|c|}\hline \rm Run & \rm [Fe]_0 & \rm [Al_2O_3]_0 & \rm [HCl]_0 &\rm initial\ rate\\\hline 1& 1.0\ M& 1.0\ M& 1.0\ M& 0.020\\\hline 2 &1.0\ M& 2.0\ M& 1.0\ M& 0.080\\\hline 3 &2.0\ M& 1.0\ M& 1.0\ M& 0. 020\\\hline 4 &3.0\ M &2.0\ M& 2.0\ M& 0.160\\\hline \end{array}
Run
1
2
3
4
[
Fe
]
0
1.0
M
1.0
M
2.0
M
3.0
M
[
A
l
2
O
3
]
0
1.0
M
2.0
M
1.0
M
2.0
M
[
HCl
]
0
1.0
M
1.0
M
1.0
M
2.0
M
initial
rate
0.020
0.080
0.020
0.160
Determining Rate Law Exponents
The following data was gathered for the reaction:
2
A
+
B
+
2
D
→
E
+
2
F
2A+B+2D\to E+2F
2
A
+
B
+
2
D
→
E
+
2
F
Find the rate law exponents and the rate constant for this reaction. Report your exponents as integers and your rate constant to two significant figures without units in the answer field.
Determining Reaction Order
Use the rate data provided to determine an experimental rate law for the following reaction.
C
H
3
M
g
B
r
+
H
2
O
→
C
H
4
+
H
O
M
g
B
r
\rm CH_3MgBr\quad+\quad H_2O\quad\overrightarrow{\hspace{1.5cm}}\quad CH_4\quad+\quad HOMgBr
C
H
3
MgBr
+
H
2
O
C
H
4
+
HOMgBr
R
u
n
[
C
H
3
M
g
B
r
]
0
[
H
2
O
]
0
i
n
i
t
i
a
l
r
a
t
e
1
0.4
M
0.2
M
0.0123
2
0.8
M
0.2
M
0.0478
3
0.8
M
0.4
M
0.0948
\begin{array}{|c|c|c|c|}\hline \rm Run &\rm [CH_3MgBr]_0 & \rm [H_2O]_0 & \rm initial\ rate\\\hline 1 & 0.4\ M & 0.2\ M & 0.0123\\\hline 2 & 0.8\ M & 0.2\ M & 0.0478\\\hline 3 & 0.8 \ M & 0.4\ M & 0.0948\\\hline \end{array}
Run
1
2
3
[
C
H
3
MgBr
]
0
0.4
M
0.8
M
0.8
M
[
H
2
O
]
0
0.2
M
0.2
M
0.4
M
initial
rate
0.0123
0.0478
0.0948
Given the following data for the
N
H
4
+
+
N
O
2
−
→
N
2
+
2
H
2
O
NH_4^+ +NO_2^- \to N_2+2H_2O
N
H
4
+
+
N
O
2
−
→
N
2
+
2
H
2
O
reaction
The rate law for the reaction is
Assume the following reaction
3
H
2
+
C
O
→
C
H
4
+
H
2
O
3H_2 +CO \to CH_4+H_2O
3
H
2
+
C
O
→
C
H
4
+
H
2
O
occurs by the given reaction mechanism.
The gas-phase reaction
2
N
O
+
2
N
H
2
→
N
2
+
2
H
2
O
2NO+2NH_2 \to N_2+2H_2O
2
N
O
+
2
N
H
2
→
N
2
+
2
H
2
O
has the following rate law expression, rate = (0.14 L
2
mol
2
s
-2
)[NO]
2
[H
2
]. If the [NO] is 0.95 M and the [H
2
] is 0.45 M, what rate is expected?
The Rate Law
For the dimerization of butadiene:
2
𝐶
4
𝐻
6
(
𝑔
)
→
𝐶
8
𝐻
12
(
𝑔
)
R
a
t
e
=
k
[
𝐶
4
𝐻
6
]
2𝐶_4𝐻_6 (𝑔) \to𝐶_8𝐻_{12} (𝑔) \qquad Rate = k [𝐶_4𝐻_6]
2
C
4
H
6
(
g
)
→
C
8
H
12
(
g
)
R
a
t
e
=
k
[
C
4
H
6
]
The units of the reaction rate are:
The Rate Law
Two reactions are both described by the equation A → products. Reaction 1 is first order with respect to [A], and Reaction 2 is second order with respect to [A]. Which option below correctly describes the initial rates of these reactions when [A] = 0.100 M?
Consider the reaction: 2A + B → C. If we determine experimentally that the overall order of this reaction is 2, which of the following options could be the differential rate law for this reaction? Select all that apply.
A proposed mechanism for the reaction of NO
2
with CO is shown below. Which of the given rate laws would accurately describe a reaction with this mechanism?
N
O
2
(
g
)
+
N
O
2
(
g
)
→
N
O
3
(
g
)
+
N
O
(
g
)
s
l
o
w
N
O
3
(
g
)
+
C
O
(
g
)
→
N
O
2
(
g
)
+
C
O
2
(
g
)
f
a
s
t
N
O
2
(
g
)
+
C
O
(
g
)
→
N
O
(
g
)
+
C
O
2
(
g
)
o
v
e
r
a
l
l
\def\arraystretch{1.5} \begin{array}{cc} NO_2(g)+NO_2(g)\to NO_3(g)+NO(g) & slow \\ NO_3(g)+CO(g)\to NO_2 (g) +CO_2 (g) & fast \\ \hline NO_2(g)+CO(g)\to NO(g)+CO_2(g) & overall \end{array}
N
O
2
(
g
)
+
N
O
2
(
g
)
→
N
O
3
(
g
)
+
N
O
(
g
)
N
O
3
(
g
)
+
C
O
(
g
)
→
N
O
2
(
g
)
+
C
O
2
(
g
)
N
O
2
(
g
)
+
C
O
(
g
)
→
N
O
(
g
)
+
C
O
2
(
g
)
s
l
o
w
f
a
s
t
o
v
er
a
l
l
Given the following data for the
N
H
4
+
+
N
O
2
−
→
N
2
+
2
H
2
O
NH_4^++NO_2^-→N_2+2H_2O
N
H
4
+
+
N
O
2
−
→
N
2
+
2
H
2
O
reaction, the rate law for the reaction is
T
r
i
a
l
[
N
H
4
+
]
[
N
O
2
–
]
R
a
t
e
1
0.010
M
0.030
M
0.020
M
/
s
2
0.015
0.030
0.030
3
0.010
0.015
0.005
\def\arraystretch{1.5} \begin{array}{c} Trial &[NH_4^+] &[NO_2^–]& Rate \\ \hline 1 & 0.010 M & 0.030 M &0.020 M/s \\ 2& 0.015& 0.030 &0.030 \\ 3&0.010 & 0.015 &0.005 \\ \end{array}
T
r
ia
l
1
2
3
[
N
H
4
+
]
0.010
M
0.015
0.010
[
N
O
2
–
]
0.030
M
0.030
0.015
R
a
t
e
0.020
M
/
s
0.030
0.005
Rate Law
For the following elementary reactions apply the Law of mass balance and write a rate law.
X
e
+
F
2
→
X
e
F
2
Xe+F_2\rightarrow XeF_2
X
e
+
F
2
→
X
e
F
2
Integrated Rate Laws
Suppose you were measuring the concentration of NOBr during this reaction:
2
N
O
B
r
→
2
N
O
+
B
r
2
2 NOBr → 2 NO + Br_2
2
N
O
B
r
→
2
N
O
+
B
r
2
The reaction is first-order with respect to [NOBr]; the initial concentration of [NOBr]
0
= 0.50M.
Chemical reaction: Rate Law
Consider the reaction given below and its experientially determined rate law. Which of the following statements is correct?
2
H
2
(
g
)
+
2
N
O
(
g
)
→
N
2
(
g
)
+
2
H
2
O
(
g
)
R
a
t
e
=
k
[
H
2
]
[
N
O
]
2
2H_2(g)+2NO(g)\to N_2(g)+2H_2O(g)\ \ \ \ \ \ \ \ Rate=k[H_2][NO]^2
2
H
2
(
g
)
+
2
N
O
(
g
)
→
N
2
(
g
)
+
2
H
2
O
(
g
)
R
a
t
e
=
k
[
H
2
]
[
N
O
]
2
The Rate law
For the reaction:
B
r
O
3
−
+
5
B
r
−
+
6
H
+
→
3
B
r
2
+
3
H
2
O
BrO_3^-+5Br^-+6H^+\to3Br_2+3H_2O
B
r
O
3
−
+
5
B
r
−
+
6
H
+
→
3
B
r
2
+
3
H
2
O
at a particular time, the rate of disappearance of Br
-
was 7.5 x 10
-2
M/s. What is the rate of disappearance of BrO
3
-
at the same instant?
The Rate Law: Half life
Radioactive plutonium Pu-241 has a half-life of 14.4 years and decays by a 1st order process. If 25 kg of Pu-241, waste from a nuclear reactor, is stored at a disposal site, how long will it take for the amount of Pu-241 to be reduced to 1 kg?
The Rate Law: Stoichiometry
If N
2
is consumed at 2 M/s, what is the production rate of NH
3
and consumption rate of H
2
in the reaction?
N
2
+
3
H
2
→
2
N
H
3
N_2\ \ +\ 3H_2\ \rightarrow\ 2\ NH_3
N
2
+
3
H
2
→
2
N
H
3
The Rate Law
For a hydrogenation reaction involving H
2
, plotting 1/[H
2
] versus time produces a straight line graph. What is the order of hydrogen in this reaction.
Chemical Kinetics
Determine the order of each reactant and the overall order for the following rate laws.
a) 𝑣 = 𝑘[𝑁𝑂][𝐶]
2
b) 𝑣 = 𝑘[𝑂
3
]
1
Determining Reaction Order
Use the rate data provided to determine an experimental rate law for the following reaction.
C
H
3
M
g
B
r
+
H
2
O
→
C
H
4
+
H
O
M
g
B
r
\rm CH_3MgBr\quad+\quad H_2O\quad\overrightarrow{\hspace{1.5cm}}\quad CH_4\quad+\quad HOMgBr
C
H
3
MgBr
+
H
2
O
C
H
4
+
HOMgBr
R
u
n
[
C
H
3
M
g
B
r
]
0
[
H
2
O
]
0
i
n
i
t
i
a
l
r
a
t
e
1
0.4
M
0.2
M
0.0123
2
0.8
M
0.2
M
0.0478
3
0.8
M
0.4
M
0.0948
\begin{array}{|c|c|c|c|}\hline \rm Run &\rm [CH_3MgBr]_0 & \rm [H_2O]_0 & \rm initial\ rate\\\hline 1 & 0.4\ M & 0.2\ M & 0.0123\\\hline 2 & 0.8\ M & 0.2\ M & 0.0478\\\hline 3 & 0.8 \ M & 0.4\ M & 0.0948\\\hline \end{array}
Run
1
2
3
[
C
H
3
MgBr
]
0
0.4
M
0.8
M
0.8
M
[
H
2
O
]
0
0.2
M
0.2
M
0.4
M
initial
rate
0.0123
0.0478
0.0948
Determining Rate Law Exponents
The following data was gathered for the reaction:
2
A
+
B
+
2
D
→
E
+
2
F
2A+B+2D\to E+2F
2
A
+
B
+
2
D
→
E
+
2
F
Find the rate law exponents and the rate constant for this reaction.
Rate Law
For the following elementary reactions apply the Law of mass balance and write a rate law.
B
2
H
6
→
2
B
H
3
B_2H_6\rightarrow 2 BH_3
B
2
H
6
→
2
B
H
3
The reaction A + 2B → products was found to follow the rate law: rate = k[A]
2
[B]. Predict by what factor the rate of reaction will increase when the concentration of A is doubled, the concentration of B is tripled, and the temperature remains constant.
By what factor does the rate change in each of the following cases?
A reaction is first order in A, and [A] is doubled
A reaction is second order in B, and [B] is halved
Determine an empirical rate law for the following reaction using the kinetic data collected at
298
K
298\ K
298
K
and evaluate the rate constant
k
k
k
.
2
F
e
+
A
l
2
O
3
+
6
H
C
l
→
F
e
2
O
3
+
2
A
l
C
l
3
+
3
H
2
O
\rm 2\ Fe\quad+\quad Al_2O_3\quad+\quad6\ HCl\quad\overrightarrow{\hspace{1.5cm}}\quad Fe_2O_3\quad+\quad2\ AlCl_3\quad+\quad3\ H_2O
2
Fe
+
A
l
2
O
3
+
6
HCl
F
e
2
O
3
+
2
AlC
l
3
+
3
H
2
O
Determining Reaction Order
Use the rate data provided to determine an experimental rate law for the following reaction.
C
H
3
M
g
B
r
+
H
2
O
→
C
H
4
+
H
O
M
g
B
r
\rm CH_3MgBr\quad+\quad H_2O\quad\overrightarrow{\hspace{1.5cm}}\quad CH_4\quad+\quad HOMgBr
C
H
3
MgBr
+
H
2
O
C
H
4
+
HOMgBr
R
u
n
[
C
H
3
M
g
B
r
]
0
[
H
2
O
]
0
i
n
i
t
i
a
l
r
a
t
e
1
0.4
M
0.2
M
0.0123
2
0.8
M
0.2
M
0.0478
3
0.8
M
0.4
M
0.0948
\begin{array}{|c|c|c|c|}\hline \rm Run &\rm [CH_3MgBr]_0 & \rm [H_2O]_0 & \rm initial\ rate\\\hline 1 & 0.4\ M & 0.2\ M & 0.0123\\\hline 2 & 0.8\ M & 0.2\ M & 0.0478\\\hline 3 & 0.8 \ M & 0.4\ M & 0.0948\\\hline \end{array}
Run
1
2
3
[
C
H
3
MgBr
]
0
0.4
M
0.8
M
0.8
M
[
H
2
O
]
0
0.2
M
0.2
M
0.4
M
initial
rate
0.0123
0.0478
0.0948
Determining Rate Law Exponents
The following data was gathered for the reaction:
2
A
+
B
+
2
D
→
E
+
2
F
2A+B+2D\to E+2F
2
A
+
B
+
2
D
→
E
+
2
F
Choose the correct rate law. For a bonus mark, solve for the rate constant (include units).
Determine an empirical rate law for the following reaction using the kinetic data collected at 298 K and evaluate the rate constant k.
A
+
B
+
C
⟶
Pr
o
d
u
c
t
s
A+B+C⟶\Pr oducts
A
+
B
+
C
⟶
Pr
o
d
u
c
t
s
[
A
]
0
(
M
)
[
B
]
0
(
M
)
[
C
]
0
(
M
)
I
n
i
t
i
a
l
R
a
t
e
(
M
/
s
)
0.151
0.213
0.398
0.480
0.251
0.105
0.325
0.356
0.151
0.213
0.525
1.102
0.151
0.250
0.480
0.988
\def\arraystretch{1.5} \begin{array}{c} \hline [A]_0 (M) &[B]_0 (M) &[C]_0 (M)&Initial \ Rate (M/s) \\ \hline 0.151 & 0.213 & 0.398 &0.480 \\ 0.251& 0.105& 0.325 &0.356 \\ 0.151&0.213 & 0.525 &1.102 \\ 0.151&0.250 &0.480 &0.988 \\ \hline \end{array}
[
A
]
0
(
M
)
0.151
0.251
0.151
0.151
[
B
]
0
(
M
)
0.213
0.105
0.213
0.250
[
C
]
0
(
M
)
0.398
0.325
0.525
0.480
I
ni
t
ia
l
R
a
t
e
(
M
/
s
)
0.480
0.356
1.102
0.988
Determine an empirical rate law for the following reaction using the kinetic data collected at
298
K
298\ K
298
K
and evaluate the rate constant
k
k
k
.
2
F
e
+
A
l
2
O
3
+
6
H
C
l
→
F
e
2
O
3
+
2
A
l
C
l
3
+
3
H
2
O
\rm 2\ Fe\quad+\quad Al_2O_3\quad+\quad6\ HCl\quad\overrightarrow{\hspace{1.5cm}}\quad Fe_2O_3\quad+\quad2\ AlCl_3\quad+\quad3\ H_2O
2
Fe
+
A
l
2
O
3
+
6
HCl
F
e
2
O
3
+
2
AlC
l
3
+
3
H
2
O
The following data tracking the concentration of reactant A was collected:
What is the order of this process with respect to A? Estimate the rate constant
Phosgene is a toxic gas prepared by the reaction of carbon monoxide with chlorine:
C
O
(
g
)
+
C
l
2
(
g
)
→
C
O
C
l
2
(
g
)
CO_{(g)}+Cl_{2(g)}\to COCl_{2(g)}
C
O
(
g
)
+
C
l
2
(
g
)
→
C
O
C
l
2
(
g
)
The following data was obtained in a kinetics study of this reaction:
Assume the following reaction
3
H
2
+
C
O
→
C
H
4
+
H
2
O
3H_2+CO→CH_4+H_2O
3
H
2
+
C
O
→
C
H
4
+
H
2
O
occurs by the given reaction mechanism. The rate law expression must be rate = ______________.
S
t
e
p
1
H
2
+
C
O
→
H
2
C
O
s
l
o
w
S
t
e
p
2
H
2
+
H
2
C
O
→
C
H
4
+
O
f
a
s
t
S
t
e
p
3
H
2
+
O
→
H
2
O
f
a
s
t
O
v
e
r
a
l
l
3
H
2
+
C
O
→
C
H
4
+
H
2
O
\def\arraystretch{1.5} \begin{array}{c} Step 1 &H_2+CO→H_2 CO&slow \\ Step 2 & H_2+H_2 CO→CH_4+O & fast \\ Step 3& H_2+O→H_2 O& fast \\ \hline Overall&3H_2+CO→CH_4+H_2 O \\ \end{array}
S
t
e
p
1
S
t
e
p
2
S
t
e
p
3
O
v
er
a
l
l
H
2
+
C
O
→
H
2
C
O
H
2
+
H
2
C
O
→
C
H
4
+
O
H
2
+
O
→
H
2
O
3
H
2
+
C
O
→
C
H
4
+
H
2
O
s
l
o
w
f
a
s
t
f
a
s
t
Assume the following reaction
3
H
2
+
C
O
→
C
H
4
+
H
2
O
3H_2 +CO \to CH_4+H_2O
3
H
2
+
C
O
→
C
H
4
+
H
2
O
occurs by the given reaction mechanism.